Foundation January 2023 Paper 1 Q16
16 80 students entered a dancing competition.
The table gives information about the length of time, in minutes, for which each student spent dancing.
| Time (\(m\)) | Frequency |
|---|---|
| \(0 \lt m \leqslant 12\) | 11 |
| \(12 \lt m \leqslant 24\) | 25 |
| \(24 \lt m \leqslant 36\) | 23 |
| \(36 \lt m \leqslant 48\) | 15 |
| \(48 \lt m \leqslant 60\) | 6 |
Work out an estimate for the mean length of time the students spent dancing.
(4)
| Scheme | Marks |
|---|---|
| 6 × 11 + 18 × 25 + 30 × 23 + 42 × 15 + 54 × 6 (= 2160) or 66 + 450 + 690 + 630 + 324 (= 2160) [lower bound products are: 0, 300, 552, 540, 288] [upper bound products are: 132, 600, 828, 720, 360] | M2 |
| “2160” ÷ “80” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 27 | A1 |
| (4) | |
| (4 marks) |
Notes
M2: for at least 4 correct products added (need not be evaluated) or
If not M2 then award:
M1 for consistent use of value within interval (including end points) for at least 4 products which must be added
or
correct midpoints used for at least 4 products and not added
M1: dep on at least M1
Allow division by their \(\Sigma f\) provided addition or total under column seen